Parameterization of Vertical Mixing in ROMS Dr. Robin Robertson School of Physical, Environmental and Mathematical Sciences
Four Major Problems in Physical Oceanography Mixing, including scale dependence and boundary enhancement, both vertical and horizontal Where and how the ocean tides are dissipated Understanding the interactions in the ocean s internal wave field Air-sea transfer, heat flux, gas exchange etc. Three of these are related to internal tides and mixing According to Wunsch [1990]
Major Sources of Ocean Mixing Wind near the surface Tides Both in the interior and near the surface Largest source of mixing for the interior ocean Contribute 1-3.2 TW (10 12 W) of energy to vertical mixing in the ocean [Garrett, 2003] Believed to maintain the vertical stratification Other Sources of Mixing Current interactions with topography Eddies Flow over sills Upwelling Biology...
Tidal Mixing Not evenly distributed Focusses in hot spots over rough topography [from Egbert and Ray, 2000]
Vertical Mixing Internal Waves are a significant mixing mechanism ~2 TW (TW=10 12 W) [Garrett, 2003; Munk and Wunsch, 1998; ] Interest in estimates of vertical mixing Measurements Difficult and expensive Small scale Episodic From Models Depends on the parameterization used Designed for boundary layer flow Fits with barotropic, but not baroclinic flow Much of mixing results from baroclinic not barotropic flows
Shortcomings of Vertical Mixing in Models Vertical Mixing Parameterization Designed only for boundary flow and local dissipation Interior shear generates little mixing in models, but significant mixing in reality, especially with lee waves Tides were/are generally ignored in climate models Now barotropic tides included in some: OFAM and BLUElink To get tidal mixing right... Not only reproduce the tides, But also reproduce the transfer of energy from the low frequencies to the high frequencies Need the mid-water column mixing
Tidal Mixing Investigation Using simulation and comparison to observations Regional Ocean Model System (ROMS) Fieberling Guyot Taken from Cushman-Roisin, 1994
Primary Vertical Mixing Parameterizations in ROMS Mellor-Yamada 2.5 level turbulence closure (MY) Large-McWilliams-Doney (LMD) Brunt-Väisälä Frequency (BVF) Generalized Ocean Mixing (GOM) Nakanishi and Niino (NN) (2006) Generic Length Scale (GLS) k (GLS:k ) k (GLS:k ) kkl (GLS:kkl) Generic (old values) (GLS:gen old) Generic (new values) (GLS:gen new) Nakanishi-Niino (NN)
Criteria for Evaluating the Performance of the Vertical Mixing Parameterization and the Model Comparison of major axes of tidal ellipses to observations to check input forcing Spectra of the velocity to check energy transfer Comparison of average diffusivity and rms difference of major axes of tidal ellipses to evaluate performance Comparison of the diffusivities against observations to check mixing Spectra of the diffusivities to evaluate how they are responding and what they are responding too
Major Axes of Tidal Ellipses M 2
Comparison against Observations
RMS Differences M 2 S 2 K 1 O 1 MY 2.57 cm s -1 1.29 cm s -1 3.16 cm s -1 1.31 cm s -1 LMD 2.55 cm s -1 1.28 cm s -1 3.23 cm s -1 1.27 cm s -1 GOM 2.69 cm s -1 1.39 cm s -1 3.11 cm s -1 1.26 cm s -1 BVF 2.61 cm s -1 1.33 cm s -1 3.23 cm s -1 1.28 cm s -1 GLS:k 2.51 cm s -1 1.25 cm s -1 3.18 cm s -1 1.26 cm s -1 GLS:k 2.56 cm s -1 1.27 cm s -1 3.21 cm s -1 1.28 cm s -1 GLS:kkl 2.57 cm s -1 1.30 cm s -1 3.21 cm s -1 1.30 cm s -1 GLS:gen new 2.52 cm s -1 1.27 cm s -1 3.18 cm s -1 1.28 cm s -1 GLS:gen old 2.54 cm s -1 1.25 cm s -1 3.18 cm s -1 1.26 cm s -1 NN 2.65 cm s -1 1.33 cm s -1 3.01 cm s -1 1.28 cm s -1
Spectra: Velocities Site of active generation
Diffusivity of Temperatures Maximum
Major Axes of Tidal Ellipses M 2
Average Vertical Diffusivity Kt Kv MY 7.6x10-4 m 2 /s 5.8x10-4 m 2 /s LMD 1.1x10-3 m 2 /s 1.0x10-3 m 2 /s GOM 1.0x10-6 m 2 /s 1.0x10-6 m 2 /s Too low BVF 1.26x10-2 m 2 /s 1.26x10-2 m 2 /s Too high GLS:k 2.3x10-3 m 2 /s 1.9x10-3 m 2 /s GLS:k 4.3x10-3 m 2 /s 3.4x10-3 m 2 /s GLS:kkl 4.2x10-4 m 2 /s 3.6x10-4 m 2 /s GLS:gen new 2.2x10-3 m 2 /s 1.6x10-3 m 2 /s GLS:gen old 4.3x10-3 m 2 /s 3.3x10-3 m 2 /s NN 2.0x10-4 m 2 /s 2.1x10-4 m 2 /s
Diffusivity over Time Diffusivity responds to the tidal cycle
Diffusivity of Temperatures Standard Deviation
Spectral Response of Diffusivities Most are white NN, MY and GLS:k- Tidal response Slightly red Spikes in NY cause high flat line LMD and most GLS Some tidal response White
And now off Eastern Australia: Tidal Simulation ROMS (Regional Ocean Model System) Bathymetry from Geoscience Australia Hydrography NODC climatology Domain covers offshore region No winds Geostrophic currents and tides only Eddies develop, of course
And now off Eastern Australian Temperature Diffusivities: Mean Tidal mixing exceeds that without tides Most mixing over the continental slope and deep features Most related to benthic stress More mixing near the diurnal critical latitudes Near O 1 critical Latitude Near K 1 critical latitude
And now off Eastern Australian Temperature Diffusivities: Standard Deviation Tidal response significant here Peaks over features Benthic response High values at all latitudes Near critical latitude, response reaches higher into water column Near O 1 critical Latitude Near K 1 critical latitude
Tidal Mixing Standard deviation of values Represents fluctuating values Tides Tidal mixing exceeds that without tides Most mixing over the outer continental shelf and slope
Comparison to Observations: Moorings Model matches observations within the 90% confidence intervals Model rolls off around 5 cpd due to horizontal resolution (4 km) Worst performance at mid levels Noise level in observations for frequencies > 10 cpd near the bottom Higher resolution simulations planned
Comparison to Observations: Moorings Match better for semidiurnals than diurnals Typical agreement for the resolution (4 km) Model overestimates below 2000 m Other daily cycles in observations in upper 500 m
Comparison to Observations: Gliders and XBT Model and Glider match well over continental shelf Boettger and Robertson 2014
Cross-Shelf Transport Tide increase the transport of cold water onto the continental shelf Positive is on shelf Latitude dependent Increases mainly during spring tide Influenced by eddies and current too This is tidal contribution equals difference of tides and no tides
Summary Vertical mixing schemes are roughly equivalent for tidal velocities Diffusivity estimates from the different vertical mixing schemes vary widely A few vertical mixing parameterizations can be eliminated Many mixing parameterizations have white responses of the diffusivities in frequency in areas of internal wave activity Many have problems with spiking: MY2.5 Best performer: Nakanishi and Niino None are designed for mid-water column mixing There is much room for improvement Need more mixing observations for evaluating mixing scheme performance
Questions
Problems with Mixing Schemes Little mid-water column diffusivity Difference in diffusivities between Mellor- Yamada and Nakanishi-Niino
Mixing Scheme for Mid-Water Column Nakanishi-Niino or Mellor-Yamada in boundary layers In area between surface and bottom forcing influence Based on K = /N 2 So K =0.75 (u z2 +v z2 ) /N 2 K =0.75 1.85x10-6 m 2 s -1 (u z2 +v z2 ) /N 2 : mixing efficiency, generally ~0.2 [Gregg, 1987] : kinematic viscosity of seawater ~1.85x10-6 m 2 s -1 Problems Vertical scale is too large in most simulations to be applicable (vertical shear average is over 100 s m) Has large spikes which affect mean value and spectra Relationship of K
Tidal Effects on Diffusivity Shear based midwater column parameterization adds mid-water column mixing in appropriate amount
Tidal Fields 8 tidal constituents simulated 4 shown here Tides very small Only exceed 1 m for M 2 very north Queensland 0.5-0.6 m for M 2 off NSW
Internal Tides and Waves
Tidal Fields Tidal currents are also small, except off of north Queensland Off NSW, only for small areas near the coast do currents exceed 2 cm s -1 Semidiurnal currents exceed diurnal currents
What Difference Does it Make in Temperature Tides make more of a difference The mid-water column mixing makes slight differences over ridge
Diffusivities Mean From a latitude study of a seamount Diffusivites peak near critical latitude High values also occur along the slope at 32.6 o S and 34.6 o S
Latitude Dependence of Temperature Diffusivities Standard Deviation From a latitude study of a seamount Diffusivites peak near critical latitude
Temperature Diffusivities Maximum Like means but larger Any observational snapshots should fall below these means
Temperature Diffusivities Difference in Standard Deviations Continental Slope Increase due to tides Largest difference just south of critical latitude Near O 1 critical Latitude Near K 1 critical latitude
Latitude Dependence of Diffusivities Generally, increases with higher latitude until critical latitudes, with one gap Also peak several degrees poleward of critical latitude Much of the integrated value is the benthic response
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